# This note is designed by the ‘Basics in Maths’ team. These notes to do help the ICSE 9^{th }class Maths students fall in love with mathematics and overcome the fear.

# These notes cover all the topics covered in the ICSE 9^{th}^{ }class Maths syllabus and include plenty of formulae and concept to help you solve all the types of ICSE 9^{th}

# Math problems asked in the CBSE board and entrance examinations.

## 1. RATIONAL AND IRRATIONAL NUMBERS

**Natural numbers: **counting numbers 1, 2, 3… called Natural numbers. The set of natural numbers is denoted by N.

N = {1, 2, 3…}

**Whole numbers: **Natural numbers including 0 are called whole numbers. The set of whole numbers denoted by W.

W = {0, 1, 2, 3…}

**Integers: **All positive numbers and negative numbers including 0 are called integers. The set of integers is denoted by I or Z.

Z = {…-3, -2, -1, 0, 1, 2, 3…}

**Rational number:** The number, which is written in the form of, where p, q are integers and q ≠ o is called a rational number. It is denoted by Q.

∗ In a rational number, the numerator and the denominator both can be positive or negative, but our convenience can take a positive denominator.

Ex: – can be written as but our convenience we can take

**Equal rational numbers:**

For any 4 integers a, b, c, and d (b, d ≠ 0), we have ⇒ ad = bc

**The order of Rational numbers:**

If are two rational numbers such that b> 0 and d > 0 then ⇒ ad > bc

**The absolute value of rational numbers:**

The absolute value of a rational number is always positive. The absolute value of is denoted by .

Ex: – absolute value of

**To find rational number between given numbers:**

**Mean method: –**A rational number between two numbers a and b is

** **Ex: – insert two rational number between 1 and 2

1 < < 2 ⟹ 1 < < 2

1 < < 2 ⟹ 1 < 2

**To rational numbers in a single step: –**

Ex:- insert two rational number between 1 and 2

To find two rational numbers, we 1 and 2 as rational numbers with same denominator 3

(∵ 1 + 2 = 3)

1 = and 2 =

Note: – there are infinitely many rational numbers between two numbers.

**The decimal form of rational numbers**

∗ Every rational number can be expressed as a terminating decimal or non-terminating repeating decimal.

**Converting decimal form into ** ** form:**

**1.Terminating decimals: –**

1.2 =

1.35 =

**2.Non-Terminating repeating decimals: –**

**Irrational numbers:**

- The numbers which are not written in the form of , where p, q are integers, and q ≠ 0 are called rational numbers. Rational numbers are denoted by Q
^{I }or S. - Every irrational number can be expressed as a non-terminating decimal or non-repeating decimal.

Ex:- and so on.

**Calculation of square roots:**- There is a reference of irrationals in the calculation of square roots in Sulba Sutra.
- Procedure to finding value:

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